Author	Loeb, Arthur L. author
Title	Concepts & Images [electronic resource] : Visual Mathematics / by Arthur L. Loeb
Imprint	Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1993
Connect to	http://dx.doi.org/10.1007/978-1-4612-0343-8
Descript	XI, 228 p. online resource

1. Introduction . 1 2. Areas and Angles . . 6 3. Tessellations and Symmetry 14 4. The Postulate of Closest Approach 28 5. The Coexistence of Rotocenters 36 6. A Diophantine Equation and its Solutions 46 7. Enantiomorphy. . . . . . . . 57 8. Symmetry Elements in the Plane 77 9. Pentagonal Tessellations . 89 10. Hexagonal Tessellations 101 11. Dirichlet Domain 106 12. Points and Regions 116 13. A Look at Infinity . 122 14. An Irrational Number 128 15. The Notation of Calculus 137 16. Integrals and Logarithms 142 17. Growth Functions . . . 149 18. Sigmoids and the Seventh-year Trifurcation, a Metaphor 159 19. Dynamic Symmetry and Fibonacci Numbers 167 20. The Golden Triangle 179 21. Quasi Symmetry 193 Appendix I: Exercise in Glide Symmetry . 205 Appendix II: Construction of Logarithmic Spiral . 207 Bibliography . 210 Index . . . . . . . . . . . . . . . . . . . . 225 Concepts and Images is the result of twenty years of teaching at Harvard's Department of Visual and Environmental Studies in the Carpenter Center for the Visual Arts, a department devoted to turning out students articulate in images much as a language department teaches reading and expressing oneยญ self in words. It is a response to our students' requests for a "handout" and to l our colleagues' inquiries about the courses : Visual and Environmental Studies 175 (Introduction to Design Science), YES 176 (Synergetics, the Structure of Ordered Space), Studio Arts 125a (Design Science Workshop, Two-Dimensionยญ al), Studio Arts 125b (Design Science Workshop, Three-Dimensional),2 as well as my freshman seminars on Structure in Science and Art

1. Introduction -- 2. Areas and Angles -- 3. Tessellations and Symmetry -- 4. The Postulate of Closest Approach -- 5. The Coexistence of Rotocenters -- 6. A Diophantine Equation and its Solutions -- 7. Enantiomorphy -- 8. Symmetry Elements in the Plane -- 9. Pentagonal Tessellations -- 10. Hexagonal Tessellations -- 11. Dirichlet Domain -- 12. Points and Regions -- 13. A Look at Infinity -- 14. An Irrational Number -- 15. The Notation of Calculus -- 16. Integrals and Logarithms -- 17. Growth Functions -- 18. Sigmoids and the Seventh-year Trifurcation, a Metaphor -- 19. Dynamic Symmetry and Fibonacci Numbers -- 20. The Golden Triangle -- 21. Quasi Symmetry -- Appendix I: Exercise in Glide Symmetry -- Appendix II: Construction of Logarithmic Spiral